It is unclear (to me, who has not studied such things in several years) where the proof uses the fact that T includes PA. Maybe it is necessary for the construction of R?
Saying that T includes PA is shorthand for the usual Gödelian requirement that T includes the basic arithmetical truths necessary to formalize the bits of common-sense reasoning used in the proof, like simulating the execution of R.
Thanks!
Saying that T includes PA is shorthand for the usual Gödelian requirement that T includes the basic arithmetical truths necessary to formalize the bits of common-sense reasoning used in the proof, like simulating the execution of R.
I figured as much; after all, in the standard proof one only needs PA around long enough to construct Goedel numbers.